R: Exponential Link Function

explink {VGAM}

R Documentation

Exponential Link Function

Description

Computes the exponential transformation, including its inverse and the first two derivatives.

Usage

explink(theta, earg = list(), inverse = FALSE, deriv = 0, short = TRUE, tag = FALSE)

Arguments

`theta`	Numeric or character. See below for further details.
`earg`	Optional list. See `Links` for general information about `earg`.
`inverse`	Logical. If `TRUE` the inverse function is computed. The inverse function is the `loge` function.
`deriv`	Order of the derivative. Integer with value 0, 1 or 2.
`short`	Used for labelling the `blurb` slot of a `vglmff-class` object.
`tag`	Used for labelling the linear/additive predictor in the `initialize` slot of a `vglmff-class` object. Contains a little more information if `TRUE`.

Details

The exponential link function is potentially suitable for parameters that are positive. Numerical values of theta close to negative or positive infinity may result in 0, Inf, -Inf, NA or NaN.

The arguments short and tag are used only if theta is character.

Value

For explink with deriv = 0, the exponential of theta, i.e., exp(theta) when inverse = FALSE. And if inverse = TRUE then log(theta); if theta is not positive then it will return NaN.

For deriv = 1, then the function returns d theta / d eta as a function of theta if inverse = FALSE, else if inverse = TRUE then it returns the reciprocal.

Here, all logarithms are natural logarithms, i.e., to base e.

Note

This function has particular use for computing quasi-variances when used with rcam and normal1.

Numerical instability may occur when theta is close to negative or positive infinity. One way of overcoming this (one day) is to use earg.

Author(s)

Thomas W. Yee

Examples

theta = rnorm(30)
explink(theta)
max(abs(explink(explink(theta), inverse = TRUE) - theta)) # Should be 0

[Package VGAM version 0.8-4 Index]